Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Dedicated to the memory of Piet Kasteleyn.     

一种蓝光发射星型有机分子的合成及光电性质

采用分子设计的思想,通过多步反应合成了一种新型的以N原子为中心的蓝光发射星型有机小分子。用1H NMR,MS和元素分析进行了表征,研究了化合物的热稳定性和真空镀膜膜层的光致发光性质,用循环伏安法测定了其电化学性能。结果表明,这种合成的有机化合物光致发光性能优良(量子效率达到87%),热稳定性好,可作为制作有机电致发光器件的候选材料。     

CM⁃Phos配体在钯催化交叉偶联反应中的应用

本文综合评述了近年来2-[2-(二环己膦基)苯基]-1-甲基-1H-吲哚(CM-Phos)膦配体及其衍生物在钯催化的交叉偶联反应中的应用, 主要根据不同种类的交叉偶联反应进行系统性分述, 并对该领域的发展前景进行了展望.     

Positivity preserving transformations for -binomial coefficients

Several new transformations for -binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found. The new -binomial transformations are also applied to obtain multisum Rogers-Ramanujan identities, to find new representations for the Rogers-Szegö polynomials, and to make some progress on Bressoud's generalized Borwein conjecture. For the original Borwein conjecture we formulate a refinement based on new triple sum representations of the Borwein polynomials.

     

“绿色”液体激光介质的非线性光学特性研究

 利用氧化钕和盐酸为原料制得Nd(phen)2Cl3(三氯二邻菲罗啉合钕),测得其光谱特性并以稀土氧化钕、苯甲酸和邻菲罗啉为原料制得绿色液体激光介质钕离子的配合物——NdB3phen（三苯甲酸—邻菲罗啉合钕）.利用飞秒激光器,采用单光束Z-扫描法研究了NdB3phen的三阶非线性光学特性.结果表明:当入射飞秒激光脉冲波长为400 nm,峰值功率密度为2.94×1014 W/m2,脉宽为117 fs时,测得样品NdB3phen的非线性折射率为－2.84×10－18 cm2/W|NdB3phen在开孔条件下呈现反饱和吸收现象,测出双光子吸收系数的值为9.11×10－12 m/W.实验结果表明,NdB3phen的双光子吸收系数和非线性折射率随着光强的增强而增大.     

A bijection which implies Melzer's polynomial identities: theχ 1,1 (p,p+1) case

We obtain a bijection between certain lattice paths and partitions. This implies a proof of polynomial identities conjectured by Melzer. In a limit, these identities reduce to Rogers-Ramanujantype identities for the _1,1 ^(p,p+1) (q) Virasoro characters, conjectured by the Stony Brook group.     

Hall–Littlewood functions and the Rogers–Ramanujan identities

We prove an identity for Hall–Littlewood symmetric functions labelled by the Lie algebra A₂. Through specialization this yields a simple proof of the A₂ Rogers–Ramanujan identities of Andrews, Schilling and the author.     

A Higher Level Bailey Lemma: Proof and Application

In a recent letter, new representations were proposed for the pair of sequences (,), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (,) labelled by the Lie algebra AN – 1, two nonnegative integers and k and a partition , whose parts do not exceed N – 1. Our results give rise to what we call a higher level Bailey lemma. As an application it is shown how this lemma can be applied to yield general q-series identities, which generalize some well-known results of Andrews and Bressoud.